experimental studies on the nature of property gradients...

Experimental studies on the nature of property gradientsin the human dentine

A. Kishen, U. Ramamurty, A. AsundiActuators and Sensors Strategic Research Program, School of Mechanical and Production Engineering, NanyangTechnological University, Singapore 639798

Received 1 July 1999; revised 29 October 1999; accepted 27 January 2000

Abstract: We conducted an investigation into the nature ofdentine mineralization and mechanical property gradientswith the aid of experimental techniques such as the fluoro-scopic X-ray microanalysis and instrumented microindenta-tion, respectively. It was found that the tooth adapts to acomplex structure with significant gradients in properties.We observed a significant correlation between the degree ofmineralization within the dentine and the mechanical prop-erties. The natural gradation in mechanical properties is ex-plained by the stress analysis within anatomical-sized tooth

specimens done using digital photoelasticity. These resultsare explained within the context of the functional require-ments that are imposed on the tooth. This study highlightstooth structure as a biologically adapted, functionallygraded material. © 2000 John Wiley & Sons, Inc. J BiomedMater Res, 51, 650–659, 2000.

Key words: digital photoelasticity; X-ray imaging; mineral-ization; microindentation; functional gradients

INTRODUCTION

Researchers have postulated that skeletal systemssuch as bone model or remodel themselves accordingto the functional requirements imposed on them.1–5

These theories have been substantiated for bone struc-tures, whose primary purpose is to carry mechanicalloads. Whether such adaptation is observed for hu-man teeth, which possess a more complex histologyand are dimensionally much smaller, has not been in-vestigated in detail.

Human teeth act as a mechanical device duringmasticatory processes such as cutting, tearing, andgrinding of food particles. However, they differ fromlong bones fundamentally in that they cannot remodelbut only adapt to its functions. Furthermore, the toothstructure exhibits significantly less blood perfusioncompared with bone. Despite those differences, fewinvestigations have studied the mechanical perspec-tives of tooth adaptation to functional forces. Devel-oping such an understanding is important for a num-ber of reasons, as discussed in the following.

Dentine structure forms the major bulk of humantooth. Recent studies have indicated dentine as a com-posite of four elements: (a) oriented tubules; (b) highlymineralized (carbonate apatite) peritubular zone; (c)collagen (type I); and (d) dentinal fluid. The majorlimitation associated with understanding the me-chanical characteristics of dentine is related to thepresence of two phases: namely, apatite and collagen,which have different mechanical properties.6 Al-though previous studies have suggested that thestrength of dentine stems from the degree of mineral-ization, the relationship between the nature of miner-alization and the associated variations in mechanicalproperties were not clear.7

Dentistry has always depended on contemporaryscience and technology for improvement in materialsand procedures. However, the principles of physicalsciences were used only in comparing physical char-acteristics of dental structures with restorative mate-rials.8 Although earlier studies highlighted anisotropyin osseous9 and dental structures,10,11 there were fewattempts made to investigate and understand the spa-tial variations in the mechanical properties of naturaltooth and characterize tooth structure as an engineer-ing material. Such an understanding will enable thedental researchers to approximate the demandsplaced on artificial restorative materials during theirfunction.

Dental practitioners have been plagued with the

Correspondence to: A/P Anand Asundi; e-mail:[email protected]

Contract grant sponsor: School of Mechanical and Produc-tion Engineering, Nanyang Technological University, Sin-gapore

© 2000 John Wiley & Sons, Inc.

problems of restoring lost tooth structure permanentlywith artificial materials. Lack of understanding of thematerial and functional characteristics of the tooth areprimarily responsible for this. Research in dental bio-materials has recognized that the tooth structure ex-hibits sophisticated anisotropy owing to its histo-physiological features. Nonetheless, no concerted ef-forts have been made to understand such anisotropy.Mechanical property measurements such as micro-hardness tests, unless conducted with caution andcare, tend to represent properties that are averagedover a large volume of the regional tissue.12 Becausethey are not able to sample individual structural com-ponents, they cannot provide information on the spa-tial variation in material characteristics of dentine.7

Consequently, numerical modeling efforts made tounderstand the stress distribution patterns in teethmake grossly simplifying assumptions. One such as-sumption is that the elastic modulus of teeth is con-stant and does not have spatial variations. Conclu-sions drawn on the basis of such studies, althoughuseful as a first step, often tend to be misleading. Thus,a good understanding of the material characteristics ofteeth is necessary before applying such knowledge inrestorative practice.

This study aimed to investigate some of these issuesand to develop an understanding of the adaptation oftooth structure to functional forces. This was achievedby using three different experimental techniques. Mi-croindentation techniques were used to assess the spa-tial gradients in the mechanical property—namely,elastic modulus and hardness along a human toothsection. A one-to-one correspondence between thesegradients and the degree of mineralization was estab-lished. The latter was measured with the aid of thefluoroscopic X-ray imaging technique. These studieswere coupled with a stress pattern analysis on ana-tomical size models using digital photoelasticity. Thisfacilitated rationalizing the adaptation of tooth struc-ture.

EXPERIMENTS

Digital photoelastic analysis

Model preparation

A human mandible with dentition, obtained from acadaver, was sectioned vertically along the symphysisregion (midline). These sections were digitized andthe coordinates were recorded. The data were sent toa computer numerical control machine to fabricatesection models of lower central incisor tooth with sup-porting mandibular bone. A photoelastic sheet (PSM-

1; Measurement Groups, NC) was used to prepare themodels.

A 0.35-mm-thick layer of silicon rubber and a 0.15-mm-thick layer of polyester composite were placedbetween the tooth and bone part of the model to simu-late the periodontal ligament and root cementum, re-spectively. Ten such models were prepared and usedseparately for each experiment.

Experimental models were divided into two groupsof five models each and were tested at 25N, 55N,125N, 150N and 200N loads. One group of models wastested for loads directed along the long axis of thetooth and the other was tested for loads at 60° lingualto the long axis of the tooth. This was done to simulatedifferent directions of occlusal forces.

Photoelastic fringe analysis

Photoelasticity is based on a stress-optic effect,which is governed by the following stress-optic law13:

s1 − s2 =u

2p?

fsh

=N ? fs

h(1)

where (s1 − s2) is the difference in the in-plane prin-cipal stress, fs is the material fringe value, h is thethickness of the specimen, u/2p is the resultant opticalphase generated owing to the stress-birefringence inthe model and, N(=u/2p) is the fringe order assignedto the dark fringes. They are nonnegative integers in atraditional dark-field polariscope. In the presentstudy, a phase-shifting method was developed for thecalculation of phase, and thus the fractional fringe or-der, at every point.

In our experiment, setting the analyzer at angles of0°, 45°, 90°, and 135° with respect to the polarizer axisinduces the required phase steps.14 The four phase-shift images [Fig. 1(A)] were evaluated using the tra-ditional phase-stepping algorithm to obtain thewrapped phase map [Fig. 1(B)].15

Phase unwrapping was done along select lines inthe wrapped image to make the fringe modulationcontinuous and provide information on the nature ofstress distribution. A circular calibration disk was ana-lyzed to calibrate and confirm the accuracy of the sys-tem (material fringe value = 6.825 KPa/fringe/m). Allmodels were tested three times for different loads(25N, 55N, 125N, 150N, and 200N) along the long axisof the tooth (0°) and 60° lingual to the long axis of thetooth.

Experimental arrangement

A special loading jig was fabricated to hold the ana-tomical scale models. A load cell was placed on thesuperior aspect of the loading device. The loading jig

651PROPERTY GRADIENTS IN HUMAN DENTINE

Figure 1. (A) Fringe patterns for the normal tooth model at150N load applied along the long axis of the tooth obtainedat four phase shifts. The angle of polarization of the analyzerwas at (a) 0°, (b) 45°, (c) 90°, and (d) 135° to that of polarizer.(B) Phase map (phase-wrapped image) obtained from thefour images shown in (A), from which the fringe orderswere calculated.

652 KISHEN, RAMAMURTY, AND ASUNDI

had individual slots that could direct forces along thelong axis (0°) and at 60° lingual to the long axis of thetooth. The loading jig and models were placed in thecircular polariscope between the first quarter waveplate (I QWP) and the second quarter wave plate (IIQWP) and the fringe patterns were recorded at vari-ous levels. Each experiment was repeated three timesfor confirmation.

Fluoroscopic X-ray microscopic image analysis

Tooth specimen preparation

Specimens were prepared from 12 permanent non-carious lower incisor teeth, stored in deionized waterat 4°C for a maximum of 2 weeks after extraction.These specimens were transilluminated before testingto exclude possibilities of cracks or extraction dam-ages. Six specimens were used to prepare a midlineplanoparallel section in the faciolingual plane and sixspecimens were used to prepare the cross-sections atthe cervical region and the apical region of the tooth.

To prepare the faciolingual sections, the specimenswere initially ground on wet emery paper of grit size180, 400, 800, and 1000 until the specimen surface wasapproximately 0.5 mm from the desired plane. Thespecimen was then polished to the final level using apolisher. Initially, diamond paste with a mean particlesize of 6 mm and later a mean particle size of 3 mm wasused during polishing to obtain a relatively smoothsurface finish for the specimens. The final specimenshad a uniform thickness of 3 mm.

To prepare the cross-sections, initially the speci-mens were sliced using a diamond cutter with wateras a coolant, followed by a systematic method, similarto the faciolingual section preparation. The preparedsections were used for fluoroscopic X-ray imageanalysis and microindentation analysis

Experiments

X-ray imaging applications are based on the rate ofabsorption of X-rays by individual atoms in a material.When X-rays are incident on a tooth specimen, differ-ential absorption takes place within the specimen. Theacquired image provides information on the varia-tions in the mineral density along the specimen.16 Inour study, fluoroscopic X-ray image analysis wasdone on the faciolingual sections and on cross-sectionsof cervical and apical region.

Figure 2 shows a schematic diagram of the Fein fo-cus X-ray microscope arrangement. The specimen wasirradiated with a 100-kV X-ray beam with a focal spotof 4 mm. The X-ray image of the specimen was pro-

duced on a fluorescent screen placed beneath thespecimen. The X-rays absorbed by the screen werere-emitted as visible light radiation of a longer wave-length, which was captured by a CCD camera. Themain advantage of digitization is that it can identifychanges in the image matrix which otherwise are notvisible to the human eye. Because the intensity (pixel)range for the digitized images fell in a narrow range,further image processing and color mapping wasdone using a conventional image processing systemfor better visualization of mineral density gradients.

Micro-indentation analysis

The micro-indentation technique enables correla-tion of material properties such as hardness and elas-tic modulus as a function of load, depth of penetra-tion, and contact pressure exerted by the microin-denter. In this experiment, microindentation analysiswas done on the faciolingual sections to examine thegradients in the elastic moduli and the hardness val-ues along the cervical, middle, and apical regions ofthe root.

Figure 3 shows a schematic diagram of the micro-indenter used in this study. During microindentationanalysis, the depth-sensing device of the system mea-sured indenter displacement (h) continuously duringloading and unloading. Figure 4 shows a schematicdiagram for a typical load-displacement curve. Thehardness (H) and the composite elastic modulus (E8)

Figure 2. Schematic diagram of the Fein focus X-ray mi-croscope.


of the confined material were determined from theload-displacement curve using Equations (2) and (3),respectively.

H =PA

(2)

E8 = Cdpdh

1

=A(3)

Where P is the indenter load, dp/dh is the slope ofload-displacement curve at the beginning of unload-ing, C is a constant (0.8756) and A is the projected areaof contact, which was determined from

A = K ? hc2 (4)

where hc is the contact depth and K is a constant (24.5)characteristic of the indenter geometry. Because E8 inEquation (3) denotes the composite modulus of thespecimen and the indenter, the specimen modulus hasto be calculated using the definition

1E8

=1 − ns

2

Es+

1 − ni2

E1(5)

where n is the Poisson’s ratio and subscript s and idenote specimen and indenter, respectively.

Experiments

Experiments to measure the hardness and modulusof elasticity of the six faciolingual sections were doneimmediately after we acquired X-ray images. Thespecimen for indentation was mounted on a glass mi-croscope slide and fixed at the margins with a smallquantity of cyanoacrylate adhesive. This was to mini-mize errors due to micromovements. A microhardnesstester fitted with a diamond (Vickers) indenter with aPoisson’s ratio of 0.07 was used to produce and mea-sure indentation in the specimen. The preliminary in-strument calibration was done based on the manufac-turer’s instructions using a standard steel specimen840 HV1 (ASTM).

Indentations were made along three lines of inter-est, perpendicular to the long axis of the specimen.These lines were chosen along the cervical, middle,and apical regions of the root (Fig. 5). The maximumnumber of indentations, spaced by 400 mm, was madealong these three lines to minimize errors due to strainhardening or propagated cracks. A load of 0.5N at aloading rate of 1N/min was used for the entire inden-tation procedure. A hold period of 15 s was insertedbefore the final unloading to diminish the viscoelasticdeformation to a negligible rate.9,17

The hardness and elastic modulus at each indentwere recorded for further analysis. Optical micro-scopic examination was done after the completion ofeach indentation to ensure the absence of any majorsurface damage in the dentine.

RESULTS

Digital photoelastic analysis: Nature ofstress distribution

Figure 1(B) shows a phase-wrapped image for thetooth and supporting bone model loaded at 150N, di-rected along the long axis of the tooth. Stress distribu-tion characteristic of bending was observed at the cer-vical region [Fig. 6(a)] and midregion of the root [Fig.Figure 4. Schematic for a typical load-displacement curve.

Figure 3. Schematic diagram of the microindenter.


6(b)], with substantially higher compressive stresseson the facial side compared with the tensile stresses onthe lingual side. Furthermore, there was a significantreduction in the bending stress toward the root apex,with only the compressive stress evident in the apicalregion [Fig. 6(c)]. The compressive stresses and tensilestresses identified during bending were reconfirmedusing a fingernail test.18 This test suggests that if theedge of the model is pressed with a fingernail or thethumbnail, compression and tensile fringes react in adistinct manner enabling them to be distinguished. Ifthe boundary stress is compressive, the fringes aredrawn toward the boundary, and if the boundarystress is tensile, the fringes moves away from theboundary. A zero-order fringe (black fringe) was alsoidentified within the tooth.

When occlusal loads of 25N, 55N, and 125N wereapplied, we found there were significant compressivestresses with negligible tensile stresses. When theloads were increased to 150N and 200N, dominantcompressive stresses persisted with small tensilestresses. There was no difference in the pattern ofstress distribution when the specimens were tested forocclusal loads directed at 60° lingual to the long axis.

Fluoroscopic X-ray imaging analysis: Nature ofmineral distribution

Figure 7(a) is a map of a typical X-ray digitizedimage along the cervical cross-section of a lower inci-

sor showing the mineralization pattern. The mineraldeposition increased gradually from the center to theouter aspect of the facial and lingual side. However,no significant mineralization was identified along themesial and distal aspects of the cross-section. No simi-lar gradient was observed in the apical region, inwhich mineral distribution was more uniform.

Figure 7(b) is a map of a typical X-ray image of alower incisor displaying mineral gradation along thefaciolingual plane. It shows a significant gradation inthe mineral density along the faciolingual plane of the

Figure 5. Horizontal and the vertical lines of interest alongthe cervical, middle, and apical regions of the root, consid-ered for material characterization in the microindentationstudies.

Figure 6. Stress distribution pattern in the normal toothmodel for a load of 150N applied along the long axis (A) inthe cervical third, (B) in the middle third, and (C) in theapical third of the root.


tooth portion. As the intensity is inversely propor-tional to the density of the specimen, Figure 8(A–C)demonstrates the mineral density gradients along thecervical, middle, and apical regions of interest, on thefaciolingual section.

The mineral density was observed to be higher onthe facial side compared with the lingual side in thefaciolingual plane. Moreover, the mineral depositiongradually increased from the center (pulp) to the outeraspect. Such gradients in mineral distribution werenot significant in the apical region of the root, whichshowed a uniformly high mineralization. However,the mineral deposition on the lingual side was dis-cernible only in the apical region of the root. Further-more, the radicular portion of the tooth exhibited aregion of minimal mineralization at the periphery.

Microindentation analysis: Gradients in hardnessand elastic modulus

Microindentation analysis provided the gradients inthe elastic modulus and hardness along the cervical,middle, and apical regions of interest in the faciolin-gual plane (Fig. 5). All specimens analyzed exhibitedidentical gradients of hardness and elastic modulus asfollows.

Cervical region

Hardness values were found to be least near thecenter and increased gradually toward the outer as-pect of the facial side. There was a noticeable drop inhardness at the outermost facial region. There was nosimilar gradient in the hardness along the lingual side.The hardness in the lingual side increased adjacent tothe center and then gradually decreased toward theouter portion [Fig. 9(a)].

The elastic modulus was also low in the region nearthe center of the tooth. The modulus value increasedconspicuously in the adjacent points of the facial andlingual side and then gradually was reduced towardthe outer aspect. Furthermore, the elastic moduluswas higher on the facial side compared with the lin-gual side [Fig. 10(a)].

Midregion

The hardness value increased gradually from thecenter to the outer aspect of the facial and lingual sideand later dropped to a lower value at the outermostregion. However, the hardness values were margin-ally higher on the facial side than the lingual side [Fig.9(b)].

Figure 7. The map of mineral density distribution along the tooth sections. (A) in the cross-section at the cervical region, and(B) midline planoparallel faciolingual section.


The elastic modulus also exhibited similar trends inits distribution. It gradually increased from the centerto the outer aspect of the facial and lingual side anddropped at the outermost indent [Fig. 10(b)].

Apical region

The apical region of the root dentine did not exhibittrends in the gradients of hardness and elastic modu-

lus as observed in the cervical and midregion [Figs.9(c) and 10(c)].

DISCUSSION

The results of microindentation experiments showthat the natural tooth exhibits complex spatial grada-tions in mechanical properties. Dentine exhibited dis-tinct gradients in elastic modulus and hardness in thefaciolingual plane. Furthermore, there was a remark-able agreement between the gradients in the elasticmodulus and the hardness values identified in the mi-

Figure 8. Mineral distribution (1/pixel) along the (A) cer-vical region (B) middle region, and (C) apical region of theroot.

Figure 9. Graph obtained from microindentation experi-ments showing typical gradients in the hardness along the(a) cervical region, (b) midregion, and (c) apical region of theroot.


croindentation experiments with the mineral distribu-tion recognized in the fluoroscopic X-ray image analy-sis. This result agrees with previous research findingsin osseous structures, where a considerable associa-tion was established between the elastic modulus andmineralization.19,20

Having established a one-to-one correspondencebetween the degree of mineralization and the me-chanical properties, it is of significant scientific impor-tance to determine why the natural tooth adapts tosuch a complicated structure. In an attempt to answerthat question, it is imperative to keep in the mind thebasic functional demands placed on the tooth.

The primary function of tooth is to act as a mechani-cal device for various masticatory activities. Conse-

quently, it tries to enhance its performance within theimposed confinement, as does any well-engineeredstructure. The confinement placed on the tooth struc-ture is primarily compatibility with the supporting al-veolar bone, which is important to avoid displacementjumps across the periodontium and thereby preventfailure of the tooth/bone system during function. An-other aspect is the long-term functional demand of thetooth. This is seemingly complicated because certainoral habits impose varying loads on the tooth. In suchsituations, an important engineering measure forlifespan would be its fatigue performance. It is wellestablished in engineering practice that for a longerfatigue life, one would need to minimize the stressconcentration and facilitate a uniform distribution ofstrain through the structure.

In the following, an effort was made to show thatthe complex spatial gradations of mechanical proper-ties observed in this work were a consequence of func-tional demands that are placed on the tooth.

The digital photoelastic experiments conducted on ahomogeneous material showed that there would besignificant bending stress in the cervical region of thetooth. The bending resulted in compressive stresses onthe facial side and tensile stresses on the lingual side ofthe neutral or zero stress region, with the maximumcompressive stresses larger than the maximum tensilestresses. This distinct distribution of compressivestress orders in the cervical and midregion of the rootwere primarily due to the geometry of the tooth. Therewas also a significant reduction in the bending stresstoward the root apex, with only the compressivestresses occurring in the apical region. This reductionin bending stress toward the root apex was a directresult of the reactant compressive forces acting on thetooth from the supporting bone.

Fluoroscopic X-ray microscopic imaging revealedthat the lower incisor tooth had a distinct mineral dis-tribution. A noticeable gradient in mineralization wasidentified in the faciolingual plane, where the mineraldensity was significantly graded in the cervical andmiddle region of the root, with mineralization gradu-ally increasing from the center to the outer aspect. Theapical region of the root did not exhibit such a gradi-ent in mineral distribution. This unique mineral dis-tribution had congruence with the distinct highercompressive stresses ascertained from digital photo-elastic analysis. The higher compressive stress on thefacial side could facilitate the natural tooth to depositmore minerals along that plane vis-a-vis the lingualside [Fig. 7(b)]. Commensurately, the facial side had ahigher modulus than the lingual side (Fig. 10). Stiff-ening of the facial side made the compressive strainslesser in the graded material vis-a-vis the homoge-neous material (as long as the stress distribution pat-tern remained the same). These results also suggestthat the tooth structure, analogous to an osseous struc-

Figure 10. Graph obtained from microindentation experi-ments showing typical gradients in the elastic modulusalong the (A) cervical region, (B) mid-third, and (C) apicalregion of the root.


ture, showed higher mineral density where increasedstrength and stiffness are required.20,21 This process ofmineralization not would only improve the mechani-cal property, but would help make the human skeletalconstituents lighter in weight.

When a vertical line of interest, as shown in Figure5, is considered, the elastic modulus increased signifi-cantly from the cervical to the apical region. The in-crease in elastic modulus was related to a taper in rootmorphology. If we assume that the Poisson’s ratio ofdentine does not depend on the mineralization,22 ahomogeneous material would result in the apical ta-pered region of the root experiencing substantiallyhigher strains than the cervical region for a given bit-ing load. Because this is unfavorable for the dento-osseous system, the dentine adaptively responds byincreasing the elastic modulus from the cervical to theapical region. Furthermore, for compatibility consid-erations, the modulus at the apical region of the roothas to be close to that of the supporting alveolar bone.The elastic-modulus/cross-sectional area ratio is moreor less a constant independent of the vertical locationalong the root. Experimental in vivo strain measure-ments by the authors on a patient undergoing end-odontic surgery revealed a significant strain reductiontoward the apical region.23 This observation is consis-tent with the aforementioned hypothesis. Hardness,which is a measure of the resistance to plastic defor-mation, does not influence the strain distribution, andhence did not vary significantly along the verticalplane.

The gradients in elastic modulus can also enhancedamage tolerance through strain distributions, asshown by Jitcharoen et al., who conducted sphericalindentation experiments on macroscopically gradedcomposites.24 Their experiments revealed that a gra-dation in modulus of elasticity (increasing linearlywith increasing depth) under the indenter fully sup-pressed the formation of Hertzian cone cracks other-wise seen in brittle materials. Suppression of crackingis not due to residual stresses, but to the stress distri-bution facilitated by the property gradients. Thesestudies suggest that functional gradation in materialsenhances resistance to contact damage and makes thematerials immune to mechanical fatigue. Because con-tact fatigue is a possible life-limiting factor,25 it is pos-sible that the tooth is adapting a graded dentine struc-ture to enhance its endurance.

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